Once upon a time, Amazon and eBay were plucky young dotcoms looking to disrupt the world of traditional, offline commerce. Nowadays, they're the giants for a new generation of startups to take aim at.

Fab.com is one of those. It started life as a social network for gay men called Fabulis, which didn't take off, before being rebooted as "design ecommerce" site Fab.com in June 2011.

It's been a meteoric rise since: the site had 1.5m registered members at the start of 2012, but now has 5m, with a fifth of those in Europe. Fab raised $40m to fuel further growth in December 2011.

That money is partly being spent on acquisitions to expand globally, with Fab having bought German company Casacanda in February 2012, and then British site Llustre in June – marking its formal launch in the UK.

"When we restarted last year, we had this confidence that we could be the best website in the world representing design," says chief executive Jason Goldberg.

"Everyday design, where people could discover products at all price points and in all categories, from home products to art and jewellery. We had an idea it was going to work, but it's been a rocket-ship so far."

The company is certainly ambitious: Goldberg talks of trying to build a "global brand like Google, Facebook or Coca-Cola" – good CEO talk, admittedly.

Why did Fab buy Llustre rather than set up shop here itself? The company looked at recruiting its own team, but Goldberg says it quickly realised that Llustre was a better fit – particularly because it was more than a mere "clone" of Fab.

"We always said that the UK market was something we should treat a little special: there's a different currency, of course, but there is also great British design here," says Goldberg.

"There are obviously Fab clones and copycats out there, but Llustre wasn't that. They built their own product and team, built a beautiful website, and we were really impressed with the relationships they build with the design community. There are designers on Llustre that we would love to have in the US."

Shellhammer says the Llustre deal will also add a new perspective to Fab – "a little softer, more ethereal, a little more British and buttoned up!" – not to mention bringing Fab the first teacups and saucers that it's ever sold.

I'm interested in the balance between local and global designers on a site like Fab: do people buy products patriotically, looking for local design first, or do they not care where items come from? Or both?

"People want to support the designers in their backyard, but they also want to collect things that are foreign and exotic," says co-founder and chief design officer Bradford Shellhammer.

"As much as people want to support their local communities, they might covet a handmade Indian rug, or ceramic speakers from Brooklyn. People love design with a worldview. But what we're trying to do is break down the perception that design is something that's elitist, exclusive and for people in the know."

Both Fab founders are big on the idea of local designers around the world finding global markets for their products, and the company posts case studies of success stories on its site to emphasise the point.

"Our mission is to bring design to as many people as possible, and democratise it, but also to take the people who make things – designers, artists, craftspeople – and allow their businesses to flourish, and to be exposed to other retailers," says Shellhammer.

One interesting point about Fab is the importance that mobile devices are playing in its growth. Mobile now accounts for 35-40% of Fab's daily visits, with 96% of those coming from its native iPhone and iPad apps.

"People who use the iPad convert to purchasers three to four times more than people on the Web, too," says Goldberg. "We have a whole group of people in our company thinking mobile-first right now, because the mobile user interacts with Fab very differently to a web user."